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Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions

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  • Jin, Xing
  • Yang, Cheng-Yu

Abstract

In this paper, we develop an efficient payoff function approximation approach to estimating lower and upper bounds for pricing American arithmetic average options with a large number of underlying assets. The crucial step in the approach is to find a geometric mean which is more tractable than and highly correlated with a given arithmetic mean. Then the optimal exercise strategy for the resultant American geometric average option is used to obtain a low-biased estimator for the corresponding American arithmetic average option. This method is particularly efficient for asset prices modeled by jump-diffusion processes with deterministic volatilities because the geometric mean is always a one-dimensional Markov process regardless of the number of underlying assets and thus is free from the curse of dimensionality. Another appealing feature of our method is that it provides an extremely efficient way to obtain tight upper bounds with no nested simulation involved as opposed to some existing duality approaches. Various numerical examples with up to 50 underlying stocks suggest that our algorithm is able to produce computationally efficient results.

Suggested Citation

  • Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.
    • Handle: RePEc:eee:finana:v:44:y:2016:i:c:p:65-77
    DOI: 10.1016/j.irfa.2016.01.009
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    1. Zhang, Hanyu & Assereto, Martina & Byrne, Julie, 2023. "Deferring real options with solar renewable energy certificates," Global Finance Journal, Elsevier, vol. 55(C).

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    More about this item

    Keywords

    American arithmetic average option; Optimal exercise time; Arithmetic average; Dimension reduction;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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